The present invention relates generally to photolithography. More specifically, the present invention relates to the simulation of an image during semiconductor manufacturing.
Photolithography is the process of transferring geometric shapes on a photographic mask to the surface of a silicon wafer; it falls under the more broad category of microlithography. A photographic mask (or xe2x80x9cphotomaskxe2x80x9d), typically a glass plate with a patterned emulsion of metal film on one side, is used in photolithography to create integrated circuits. Chromium (chrome) is typically used to produce the pattern on the photomask.
The successful manufacture of advanced sub-micron sized semiconductor devices requires accuracy in production of the photomask, and in the photolithography processes used to pattern the wafer. Photolithography processes for semiconductor manufacturing frequently use image simulation for predicting the outcome of the manufacturing process. Simulation allows an evaluation of the quality of the product before spending time and money producing the actual product. The simulation takes as input either the electronic, geometrical design of the circuit to be produced, or the observed photomask image made from that design. The output is either a representation of the image as formed on the resist on the wafer, the so-called xe2x80x9caerial image,xe2x80x9d or a representation of the result after the wafer has been exposed and developed.
The current standard procedure, as implemented in products such as VSS by Numerical Technologies, Inc. and ProLith by KLA-Tencor, is to use the Hopkins Method for modeling the electric fields that create the final image on the wafer. The Hopkins method is described in the following references, which are incorporated by reference: the Kirchauer Thesis available at http://www.iue.tuwien.ac.at/publications/PhD%20Theses/kirchauer/node62.html; Professor Neurcuther""s work on UC Berkeley""s xe2x80x9cSPLATxe2x80x9d simulation programi, available at http//cuervo.ccs.berkeley.edu/Volcano/applications/Defect/directory.html; and A. K. Wong and A. R. Neureuther, Rigorous Three-Dimensional Time-Domain Finite-Difference Electromagnetic Simulation for Photolithographic Applications, IEEE Trans. Semicond. Manufact., 8(4):419-431, November 1995).
The Hopkins Method requires a large number of calculations, and therefore is quite slow. A faster technique for simulating an image would be highly desirable. Faster simulation is important anywhere simulation is used. In photomask defect detection and analysis it allows determination of defect severity on the resultant wafer at a rate similar to the speed of current mask inspection machines. This greatly reduces the number of false defects reported while increasing the available sensitivity of inspections. Reduced false defect reports decreases costs involved with 1) reviewing reported defects 2) repairing false defects 3) damage caused by repair, and 4) re-inspecting masks after repair. Increasing sensitivity allows using existing inspection machines for newer, smaller geometry chip designs.
Fast simulation is also important for chip design and photolithography process development. A faster simulation method would allow more iterations of a chip design to optimize feature placement and optical enhancement techniques. It would also allow more of a chip""s logic to be simulated to verify correct operation in the finished product.
To achieve the foregoing, and in accordance with the purpose of the present invention, a fast method of simulating the results of imaging and wafer processing using conventional image processing techniques is disclosed. The present invention uses conventional image processing techniques to produce an improved result with less computation. A typical speed increase is 5000xc3x97 compared to the Hopkins Method.
This method models two optical processes to produce an accurate simulation more quickly: blurring and edge diffraction. Blurring is introduced by the optical resolution of the projection lens. This is defined in optical texts as the Rayleigh resolution criterion: Res=/0.61xcex/NA, where xcex is the wavelength of light used in the microscope, and NA is the Numerical Aperture of the main microscope lens, a measure of the lens""s diameter. NA is defined as NA=n/2f#, where n is the index of refraction of the glass, and f# is the ratio of the lens focal length to its diameter. Edge diffraction, as defined in elementary physics texts, causes opaque areas to appear larger in a microscope than if measured mechanically. The nature of this edge diffraction is that photons that graze close to the edge of an opaque area get diffracted away from the microscope objective lens, causing the opaque area to appear larger optically than it is physically. Convolution with a gaussian kernel simulates the blurring; erosion and dilation simulate the edge diffraction.
Convolution and deconvolution are known image processing techniques that can be performed by several methods, as described in The Image Processing Handbook, by John C. Russ, CRC Press, 1992, incorporated herein by reference.
Erosion is a known image processing technique and may be performed by replacing each pixel with the darkest of the nine pixels adjacent to it, including itself. Dilation is the opposite function, replacing each pixel with the brightest of the nine pixels adjacent to it, including itself. References to methods of performing erosion apply to dilation by replacing xe2x80x9cminimumxe2x80x9d by xe2x80x9cmaximum.xe2x80x9d In the literature these are referred to as gray scale erosion and gray scale dilation in xe2x80x9cThe Image Processing Handbookxe2x80x9d mentioned above.
In a first embodiment of the invention, the transmission optical source image of the photomask is deconvolved to remove optical blurring, which is then dilated to remove edge diffraction as described above. This produces a simulated physical image corresponding to a theoretical infinite resolution optical microscope. This intermediate simulated physical image is eroded, and then convolved according to the resolution of the stepper at the photomask plane. This convolution produces a simulated image projected onto the wafer, or a xe2x80x9csimulated wafer aerial image.xe2x80x9d This aerial image can then be further eroded to match the effects of resist and developing, producing a xe2x80x9csimulated wafer resist image.xe2x80x9d Optional thresholding may be performed on the simulated wafer resist image to produce a simulated processed wafer image. Thresholding is described in Russ mentioned above, incorporated by reference herein.
In a second embodiment of the invention useful in practice, several steps are combined. The microscope resolution is typically two to three times higher than the stepper resolution being simulated. This fact allows steps to be combined because deconvolution as a separate step is not required. Thus, the deconvolution step may be eliminated by reducing the amount of blurring used to produce the aerial image. In addition, the dilation and erosion steps used to produce the aerial image are combined into a single erosion.
Where a phase shift mask is involved, a complex convolution is used. A phase shift mask has areas where the glass substrate is thinned, usually by an amount that causes the light to be delayed by xc2xd wavelength, or a phase of 180 degrees. This phase shift of 180 degrees causes dark destructive interference at the edge between the shifted and unshifted areas. The interference causes edges to appear sharper on the wafer, and that allows for more focus and illumination error during printing while yielding good devices. This technique is explained in Kirchauer, cited above.
Complex convolution is the same as standard convolution except that the data (images and kernel) are complex numbers that represent magnitude and phase. The pixel values in the source image are converted from energy to voltage by taking the square root. At the end the pixel values are squared to convert voltage back to energy or magnitude. Basically, an image is converted to complex values (electric field and phase) where there is a fixed phase difference between the clear and dark regions. This requires knowing the design phase difference (typically 180 degrees) and transmission through the dark areas, typically 0% or 6% of the clear transmission, depending on the type of phase shift mask at the stepper wavelength. Other values of phase shift and transmission can be simulated, although the literature does not discuss their use at this time.
The source image is then adjusted by replacing the original dark area values by the design transmission values, and then setting the phase information by setting it to zero typically for the clear pixels, and setting it to the design phase for the dark pixels. In alternating type phase shift masks the phase of the dark areas is set to zero, and the clear areas arc set alternately to zero and the design phase. The convolution kernel has a gaussian intensity distribution, and an optional phase part that corresponds to the illumination partial coherence, as described in Kirchauer, above. After the complex convolution the pixel values are squared to convert the electric field values back to energy or intensity.
Thus, a fast image simulation results. Using the ProLith product from KLA-Tencor on similar images, for example, an image can be simulated 1,000 times faster while using a CPU fourteen times slower (total of 14,000 times faster) than reported by Intel Corporation in Primadonna: A System For Automated Defect Disposition Of Production Masks Using Wafer Lithography Simulation, by Dan Bald et al., SPIE Bacus 2002. Further, the source data can come from an image generated from the photomask electronic design or from an optical or non-optical (such as SEM, FIB, AFM) image of the actual photomask.
The simulated image may then be used to calculate edge position errors, CD errors, feature position errors and contrast errors. Because the simulation occurs much more quickly, these measurements can be used to decrease false defect reports from inspection tools, and to allow for increased sensitivity of inspection tools. A faster simulation also helps to accelerate process development for new products by allowing more variables to be tried, and improves OPC (optical proximity correction) techniques as more adjustments can be tried.